In this work, we present the electronic structure of Cadmiun Telluride (CdTe) and Mercury Teluride (HgTe), obtained using the local spin density approximation, including the Hubbard correction (LSDA+U), in the density functional theory (DFT), considering non relativistic, relativistic, and relativistic with spin-orbit coupling effects for each alloy. The results show that relativistic effects reduce the band gap for both alloys, and inverted band ordering for HgTe is only possibe if spin-orbit copupling is considered.